| Original Message (ID '224113') By samaneh: |
| In Response To 'Re: convex optimization problem'
---------
Dear Bill,
Thanks for your email. S2 is a desicion variable that we want to find it from this optimization problem. So we do not know it.
The procedure for find it could be like this:
after finding s1= argmin (c1(s1),s1)as a optimal solution of c1, in second step we want to find s2 which is s2=argminC2(y2, S1)
I correct some mistakes which already done, here is the new codes: but it dose not work well.
I attach the original problem, may be to put in mathematica I make a mistake.
I would be grateful if you please guide me.
thanks
Clear[x, s1]; Remove[c1]
h1 = 0.5; b1 = 10; \[Mu] = 10; \[Sigma] = 5; l1 = 5; l2 = 5; h2 = 0.5;
\[Mu]1 = (l1 + 1)*\[Mu];
\[Sigma]1 = Sqrt[l1 + 1]*\[Sigma];
\[Mu]2 = (l2 + 1)*\[Mu];
\[Sigma]2 = Sqrt[l2 + 1]*\[Sigma];
\[Mu]3 = (l2)*\[Mu];
\[Sigma]3 = Sqrt[l2]*\[Sigma];
c1 = Integrate[
h1*(s1 - x)*PDF[NormalDistribution[\[Mu]1, \[Sigma]1], x], {x, 0,
s1}] +
Integrate[(b1 + h1 + h2)*(x - s1)*
PDF[NormalDistribution[\[Mu]1, \[Sigma]1], x], {x, s1, Infinity}]
NMinimize[c1, s1]
w = NArgMin[c1, s1];
Print["s1=", w];
cost1 = NMinValue[c1, s1];
Print["cost1=", cost1];
c2 = h2*(s2 - \[Mu]2) + cost1 -
Integrate[
cost1*PDF[NormalDistribution[\[Mu]3, \[Sigma]3], u], {u, s2 - w,
Infinity}] +
h1*Integrate[(s2 - u - x)*
PDF[NormalDistribution[\[Mu]1, \[Sigma]1], x]*
PDF[NormalDistribution[\[Mu]3, \[Sigma]3], u], {x, 0, s2 - u} {u,
s2 - w, Infinity}] +
(b1 + h1 + h2)*
Integrate[(x - s2 + u)*
PDF[NormalDistribution[\[Mu]1, \[Sigma]1], x]*
PDF[NormalDistribution[\[Mu]3, \[Sigma]3], u], {x, s2 - u,
Infinity} {u, s2 - w, Infinity}]
NMinimize[c2, s2]
some error:
Integrate::ilim: Invalid integration variable or limit(s) in {u x,0,(s2-u) \[Infinity]}. >>
Integrate::ilim: Invalid integration variable or limit(s) in {u x,(-80.9637+s2) (s2-u),\[Infinity]}. >>
Integrate::ilim: Invalid integration variable or limit(s) in {u x,0,(s2-u) \[Infinity]}. >>
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